In this paper, we propose an algorithm to find centers of clusters based on adjustable entropy technique. A completely differentiable non-convex optimization model for the clustering center problem is constructed. A parameter free filled function method is adopted to search for a global optimal solution of the optimization model. The proposed algorithm can avoid the numerical overflow phenomenon. Numerical results illustrate that the proposed algorithm can effectively hunt centers of clusters and especially improve the accuracy of the clustering even with a relatively small entropy factor.